One thesis in regards to the vitality of religions is that state sponsorship tends to result in disaffection because public monopolies offer sub-standard product. In contrast, separation between the public sector and religion results in a free market of ideas which promotes vigorous diversity and competition which satisfies the tastes of all (or nearly all). Below is a map from Wikipedia which shows "state religions" by geography. I don't think I accept the predictive power of the thesis above....
How you define "state religion" can be a little sketchy, but usually it has to be privileges and recognition in the constitution or laws of a nation. By contrast, the Netherlands has no state religion but does subsidize religious schools, while Germany has a voluntary church tax which smooths the revenue stream for Protestants and Catholics. But in neither of these cases do the entanglements reach the level of state establishment of a particular religion.
